We introduce the concept of “quantum geometric nesting” (QGN) to characterize the idealized ordering tendencies of certain flat-band systems implicit in the geometric structure of the flat-band subspace. Perfect QGN implies the existence of an infinite class of local interactions that can be explicitly constructed and give rise to solvable ground states with various forms of possible fermion bilinear order, including flavor ferromagnetism, density waves, and superconductivity. For the ideal Hamiltonians constructed in this way, we show that certain aspects of the low-energy spectrum can also be exactly computed including, in the superconducting case, the phase stiffness. Examples of perfect QGN include flat bands with certain symmetries (e.g., chiral or time reversal) and non-symmetry-related cases exemplified with an engineered model for pair-density wave. Extending this approach, we obtain exact superconducting ground states with nontrivial pairing symmetry.

中文翻译：

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“量子几何嵌套”和可解模型平带系统


我们引入了“量子几何嵌套”（QGN） 的概念来描述平带子空间的几何结构中隐含的某些平带系统的理想化排序趋势。完美 QGN 意味着存在无限类的局部相互作用，这些相互作用可以显式构造并产生具有各种可能的费米子双线性级的可解基态，包括风味铁磁性、密度波和超导性。对于以这种方式构建的理想哈密顿量，我们表明也可以精确计算低能谱的某些方面，包括在超导情况下的相位刚度。完美 QGN 的示例包括具有某些对称性（例如，手性或时间反转）的平坦带和非对称性相关情况，例如以对密度波的工程模型为例。扩展这种方法，我们获得了具有非平凡配对对称性的精确超导基态。